Determining resistivity of a formation adjacent to a borehole having casing by generating constant current flow in portion of casing and using at least two voltage measurement electrodes

ABSTRACT

Methods of operation of different types of multiple electrode apparatus vertically disposed in a cased well to measure information related to the resistivity of adjacent geological formations from within the cased well are described. The multiple electrode apparatus has a minimum of two spaced apart voltage measurement electrodes that electrically engage a first portion of the interior of the cased well and that provide at least first voltage information. Current control means are used to control the magnitude of any selected current that flows along a second portion of the interior of the casing to be equal to a predetermined selected constant. The first portion of the interior of the cased well is spaced apart from the second portion of the interior of the cased well. The first voltage information and the predetermined selected constant value of any selected current flowing along the casing are used in part to determine a magnitude related to the formation resistivity adjacent to the first portion of the interior of the cased well. Methods and apparatus having a plurality of voltage measurement electrodes are disclosed that provide voltage related information in the presence of constant currents flowing along the casing which is used to provide formation resistivity.

This invention was made with Government support under DOE Grant No.DE-FG06-84ER13294, entitled "Validating the Paramagnetic LoggingEffect", Office of Basic Energy Sciences, of the U.S. Department ofEnergy. The government has certain rights in this invention. The basicconcept for the invention described herein was conceived during thefunding provided by the above grant.

Ongoing research to measure resistivity through casing has been providedon a co-funded basis from: (a) U.S. Department of Energy Grant No.DE-FG19-88BC14243 entitled "Proof of Feasibility of Thru CasingResistivity Technology"; (b) U.S. Department of Energy (DOE) Grant No.DE-FG22-90BC14617 entitled "Proof of Concept of Moving Thru CasingResistivity Apparatus"; (c) U.S. Department of Energy Grant No.DE-FG22-93BC14966 entitled "Fabrication and Downhole Testing of MovingThrough Casing Resistivity Apparatus"; and (d) Gas Research Institute(GRI) Contract No. 5088-212-1664 entitled "Proof of Feasibility of theThrough Casing Resistivity Technology". The government and the GRI havecertain rights in this invention. The application herein was filedduring periods of time funded by (b) and (c) above.

This application is a Divisional Application of an earlier, and stillpending, Continuation-in-Part Application that is entitled "DeterminingResistivity of a Formation Adjacent to a Borehole Having Casing UsingMultiple Electrodes and With Resistances Being Defined Between theElectrodes"; which is Ser. No. 08/083,615; which has a filing date ofJun. 28, 1993; and which issued on Oct. 29, 1996 as U.S. Pat. No.5,570,024 {"Vail(024)"}. An entire copy of Ser. No. 08/083,615 isincluded herein by reference. Ser. No. 08/083,615 is aContinuation-in-Part Application of an earlier Divisional Applicationthat is entitled "Methods of Operation of Apparatus Measuring FormationResistivity From Within A Cased Well Having One Measurement and TwoCompensation Steps"; which is Ser. No. 07/754,965; which has a filingdate of Sep. 4, 1991; and that issued on Jun. 29, 1993 as U.S. Pat. No.5,223,794 {"Vail(794)"}. An entire copy of Ser. No. 07/754,965 isincluded herein by reference.

Ser. No. 07/754,965 is a Divisional Application of an earlierContinuation-in-Part Application that is entitled "ElectronicMeasurement Apparatus Movable In A Cased Borehole and Compensating forCasing Resistance Differences"; which is Ser. No. 07/434,886, which hasa filing date of Nov. 13, 1989; and which issued on Dec. 24, 1991 asU.S. Pat. No. 5,075,626 {"Vail(626)"}. An entire copy of Ser. No.07/434,886 is included herein by reference.

Ser. No. 07/434,886 is a Continuation-in-Part Application of an earlierContinuation-in-Part Application having the title of "Methods andApparatus for Measurement of Electronic Properties of GeologicalFormations Through Borehole Casing"; which is Ser. No. 07/089,697; whichhas the Filing Date of Aug. 26, 1987; and which issued on Nov. 21, 1989as U.S. Pat. No. 4,882,542 {"Vail(542)"}. An entire copy of Ser. No.07/089,697 is included herein by reference.

Ser. No. 07/089,697 is a Continuation-in-Part Application of theoriginal Parent Application having the title "Methods and Apparatus forMeasurement of the Resistivity of Geological Formations from WithinCased Boreholes"; which is Ser. No. 06/927,115; which has the FilingDate of Nov. 4, 1986; and which issued on Apr. 11, 1989 as U.S. Pat. No.4,820,989 {"Vail(989)"}. An entire copy of Ser. No. 06/927,115 isincluded herein by reference. In addition to the above issued patentsand co-pending applications, there are yet three additional U.S. patentsthat have issued which are related to the above applications,respectively (i), (ii), and (iii), that are defined by the following.(i) U.S. Pat. No. 5,043,669 {"Vail(669)"} entitled "Methods andApparatus for Measurement of the Resistivity of Geological FormationsFrom Within Cased Wells in Presence of Acoustic and Magnetic EnergySources"; that issued on Aug. 27, 1991; that is Ser. No. 07/438,268;that has the filing date of Nov. 16, 1989; and that is aContinuation-in-Part Application of Ser. No. 07/089,697. An entire copyof Ser. No. 07/438,268 is included herein by reference.

(ii) U.S. Pat. No. 5,043,668 {"Vail(668)"} entitled "Methods andApparatus for Measurement of Electronic Properties of GeologicalFormations Through Borehole Casing"; that issued on Aug. 27, 1991; thatis Ser. No. 07/435,273; that has the filing date of Oct. 30, 1989; andthat is a Continuation Application of Ser. No. 07/089,697. An entirecopy of Ser. No. 07/435,273 is included herein by reference.

(iii) U.S. Pat. No. 5,187,440 {"Vail(440)"} entitled "MeasuringResistivity Changes From Within a First Cased Well to Monitor FluidsInjected Into Oil Bearing Geological Formations From A Second Cased WellWhile Passing Electrical Current Between the Two Cased Wells"; thatissued on Feb. 16, 1993; that is Ser. No. 07/749,136; that has thefiling date of Aug. 23, 1991; and that is a Continuation-in-PartApplication of Ser. No. 07/435,273. An entire copy of Ser. No.07/749,136 is included herein by reference.

This invention provides improved methods and apparatus for measurementof the electronic properties of formations such as the resistivities,polarization phenomena, and dielectric constants of geologicalformations and cement layers adjacent to cased boreholes and formeasuring the skin effect of the casing present. The terms "electronicproperties of formations" and "electrochemical properties of formations"are used interchangeably herein.

The oil industry has long sought to measure resistivity through casing.Such resistivity measurements, and measurements of other electrochemicalphenomena, are useful for at least the following purposes: locatingbypassed oil and gas; reservoir evaluation; monitoring water floods;measuring quantitative saturations; cement evaluation; permeabilitymeasurements; and measurements through a drill string attached to adrilling bit. Therefore, measurements of resistivity and otherelectrochemical phenomena through metallic pipes, and steel pipes inparticular, are an important subject in the oil industry. Many U.S.patents have issued in the pertinent Subclass 368 of Class 324 of theUnited States Patent and Trademark Office which address this subject.The following presents a brief description of the particularly relevantprior art presented in the order of descending relative importance.

U.S. patents which have already issued to the inventor in this field arelisted as follows: U.S. Pat. No. 4,820,989 (Ser. No. 06/927,115); U.S.Pat. No. 4,882,542 (Ser. No. 07/089,697); U.S. Pat. No. 5,043,668 (Ser.No. 07/435,273); U.S. Pat. No. 5,043,669 (Ser. No. 07/438,268); U.S.Pat. No. 5,075,626 (Ser. No. 07/434,886); U.S. Pat. No. 5,187,440 (Ser.No. 07/749,136) U.S. Pat. No. 5,223,794 (Ser. No. 07/754,965); and Ser.No. 08/083,615 that is to issue as U.S. Pat. No. 5,570,024 on Oct. 29,1996. These eight U.S. Patents are collectively identified as "the VailPatents" herein.

The apparatus and methods of operation herein disclosed are embodimentsof the Through Casing Resistivity Tool® that is abbreviated TCRT®. TheThrough Casing Resistivitv Tool® and TCRT® are Trademarks ofParaMagnetic Logging, Inc. in the United States Patent and TrademarkOffice. ParaMagnetic Logging, Inc. has its principal place of businesslocated at 18730-142nd Avenue N.E., Woodinville, Wash., 98072, USA,having telephone number (206) 481-5474.

An important paper concerning the Through Casing Resistivity Tool waspublished recently. Please refer to the article entitled "FormationResistivity Measurements Through Metal Casing", having authors of W. B.Vail, S. T. Momii of ParaMagnetic Logging, Inc., R. Woodhouse ofPetroleum and Earth Science Consulting, M. Alberty and R. C. A. Peveraroof BP Exploration, and J. D. Klein of Arco Exploration and ProductionTechnology which appeared as Paper "F", Volume I, in the Transactions ofthe SPWLA Thirty-Fourth Annual Logging Symposium, Calgary, Alberta,Canada, Jun. 13-16, 1993, sponsored by The Society of Professional WellLog Analysts, Inc. of Houston, Tex. and the Canadian Well LoggingSociety of Calgary, Alberta, Canada (13 pages of text and 8 additionalfigures). Experimental results are presented therein which confirm thatthe apparatus and methods disclosed in Ser. No. 07/434,886 that is U.S.Pat. No. 5,075,626 actually work in practice to measure the resistivityof geological formations adjacent to cased wells. To the author'sknowledge, the SPWLA paper presents the first accurate measurements ofresistivity obtained from within cased wells using any previousexperimental apparatus.

Other articles appearing in various publications concerning the ThroughCasing Resistivity Tool and/or the Vail Patents include the followinguntil the filing date of the parent of this Divisional Application,i.e., to the date of Jun. 28, 1993: (A) in an article entitled"Electrical Logging: State-of-the-Art" by Robert Maute of the MobilResearch and Development Corporation, in The Log Analyst, Vol. 33, No.3, May-June 1992 page 212-213; and (B) in an article entitled "ThroughCasing Resistivity Tool Set for Permian Use" in Improved Recovery Week,Volume 1, No. 32, Sep. 28, 1992.

The Vail Patents describe the various embodiments of the Through CasingResistivity Tool (TCRT). Many of these Vail Patents describe embodimentsof apparatus having three or more spaced apart voltage measurementelectrodes which engage the interior of the casing, and which also havecalibration means to calibrate for thickness variations of the casingand for errors in the placements of the voltage measurement electrodes.

U.S. Pat. No. 4,796,186 which issued on Jan. 3, 1989 to Alexander A.Kaufman entitled "Conductivity Determination in a Formation Having aCased Well" also describes apparatus having three or more spaced apartvoltage measurement electrodes which engage the interior of the casingand which also have calibration means to calibrate for thicknessvariations in the casing and for errors in the placements of theelectrodes. This patent has been assigned to ParaMagnetic Logging, Inc.of Woodinville, Wash. In general, different methods of operation andanalysis are described in the Kaufman Patent compared to the VailPatents cited above.

U.S. Pat. No. 4,837,518 which issued on Jun. 6, 1989 to Michael F. Gard,John E. E. Kingman, and James D. Klein, assigned to the AtlanticRichfield Company, entitled "Method and Apparatus for Measuring theElectrical Resistivity of Geologic Formations Through Metal Drill Pipeor Casing", predominantly describes two voltage measurement electrodesand several other current introducing electrodes disposed verticallywithin a cased well which electrically engage the wall of the casing,henceforth referenced as "the Arco Patent". However, the Arco Patentdoes not describe an apparatus having three spaced apart voltagemeasurement electrodes and associated electronics which takes thevoltage differential between two pairs of the three spaced apart voltagemeasurement electrodes to directly measure electronic propertiesadjacent to formations. Nor does the Arco Patent describe an apparatushaving at least three spaced apart voltage measurement electrodeswherein the voltage drops across adjacent pairs of the spaced apartvoltage measurement electrodes are simultaneously measured to directlymeasure electronic properties adjacent to formations. Therefore, theArco Patent does not describe the methods and apparatus disclosedherein.

USSR Patent No. 56,026, which issued on Nov. 30, 1939 to L. M. Alpin,henceforth called the "Alpin Patent", which is entitled "Process of theElectrical Measurement of Well Casings", describes an apparatus whichhas three spaced apart voltage measurement electrodes which positivelyengage the interior of the casing. However, the Alpin Patent does nothave any suitable calibration means to calibrate for thicknessvariations of the casing nor for errors related to the placements of thevoltage measurement electrodes. Therefore, the Alpin Patent does notdescribe the methods and apparatus disclosed herein.

French Patent No. 2,207,278 having a "Date of Deposit" of Nov. 20, 1972(hereinafter "the French Patent") describes apparatus having four spacedapart voltage measurement electrodes which engage the interior ofborehole casing respectively defined as electrodes M, N, K, and L.Various uphole and downhole current introducing electrodes aredescribed. Apparatus and methods of operation are provided thatdetermines the average resistance between electrodes M and L. ThisFrench Patent further explicitly assumes an exponential current flowalong the casing. Voltage measurements across pair MN and KL are thenused to infer certain geological parameters from the assumed exponentialcurrent flow along the casing. However, the French Patent does not teachmeasuring a first casing resistance between electrodes MN, does notteach measuring a second casing resistance between electrodes NK, anddoes not teach measuring a third casing resistance between electrodesKL. The invention herein and other preferred embodiments described inthe Vail Patents teach that it is of importance to measure said first,second, and third resistances to compensate current leakage measurementsfor casing thickness variations and for errors in placements of thevoltage measurement electrodes along the casing to provide accuratemeasurements of current leakage into formation. Further, manyembodiments of the Vail Patents do not require any assumption of theform of current flow along the casing to measure current leakage intoformation. Therefore, for these reasons alone, the French Patent doesnot describe the methods and apparatus disclosed herein. There are manyother differences between various embodiments of the Vail Patents andthe French Patent which are described in great detail in the Statementof Prior Art for Ser. No. 07/754,965 dated Dec. 2, 1991 issued as U.S.Pat. No. 5,223,794 on Jun. 29, 1993.

An abstract of an article entitled "Effectiveness of Resistivity Loggingof Cased Wells by A Six-Electrode Tool" by N. V. Mamedov was referencedin TULSA ABSTRACTS as follows: "IZV.VYSSH.UCHEB, ZAVEDENII, NEFT GAZ no.7, pp. 11-15, July 1987. (ISSN 0445-0108; 5 refs, in Russian)",hereinafter the "Russian Article". It is the applicant's understandingfrom an English translation of that Russian Article that the articleitself mathematically predicts the sensitivity of the type tooldescribed in the above defined French Patent. The Russian Article statesthat the tool described in the French Patent will only be show a "weakdependence" on the resistivity of rock adjacent to the cased well. Bycontrast, many embodiments of the Vail Patents, and the inventionherein, provide measurements of leakage current and other parameterswhich are strongly dependent upon the resistivity of the rock adjacentto the cased well. Therefore, this Russian Article does not describe themethods and apparatus disclosed herein.

U.S. Pat. No. 2,729,784, issued on Jan. 3, 1956 having the title of"Method and Apparatus for Electric Well Logging", and U.S. Pat. No.2,891,215 issued on Jun. 16, 1959 having the title of "Method andApparatus for Electric Well Logging", both of which issued in the nameof Robert E. Fearon, henceforth called the "Fearon Patents", describeapparatus also having two pairs of voltage measurement electrodes whichengage the interior of the casing. However, an attempt is made in theFearon Patents to produce a "virtual electrode" on the casing in anattempt to measure leakage current into formation which provides formethods and apparatus which are unrelated to the Kaufman and VailPatents cited above. The Fearon Patents neither provide calibrationmeans, nor do they provide methods similar to those described in eitherthe Kaufman Patent or the Vail Patents, to calibrate for thicknessvariations and errors in the placements of the electrodes. Therefore,the Fearon Patents do not describe the methods and apparatus disclosedherein.

Accordingly, an object of the invention is to provide new and practicalapparatus having three or more spaced apart voltage measurementelectrodes to measure formation resistivity from within cased wells.

It is yet another object of the invention is to provide new methods ofoperation of the multi-electrode apparatus to measure formation fromwithin cased wells which compensates for casing resistance differencesand which compensates for errors in placements of the voltagemeasurement electrodes.

FIG. 1 is a sectional view of one preferred embodiment of the inventionof the Through Casing Resistivity Tool (TCRT) which is marked with thelegend "Prior Art".

FIG. 2 shows ΔI vs. Z which diagrammatically depicts the response of thetool to different formations which is marked with the legend "PriorArt".

FIG. 3 is a sectional view of a preferred embodiment of the inventionwhich shows how V_(o) is to be measured that is marked with the legend"Prior Art".

FIG. 4 is a sectional view of an embodiment of the invention which hasvoltage measurement electrodes which are separated by differentdistances that is marked with the legend "Prior Art".

FIG. 5 is a sectional view of an embodiment of the invention which haselectrodes which are separated by different distances and which showsexplicitly how to measure V_(o) that is marked with the legend "PriorArt".

FIG. 6 is a sectional view of an embodiment of the invention whichprovides multi-frequency operation to compensate for errors ofmeasurement marked with the legend "Prior Art".

FIG. 7 is a sectional view of an embodiment of the invention thateliminates the use of a certain differential amplifier.

FIG. 8 is a sectional view of an embodiment of the invention thatpossesses four spaced apart voltage measurement electrodes.

FIG. 9 is a sectional view of an embodiment of the invention thatpossesses four spaced apart voltage measurement electrodes and extracurrent introducing electrodes.

FIG. 10 is a multi-electrode apparatus designed to keep certain currentsflowing along the casing constant in amplitude in the vicinity of fourspaced apart voltage measurement electrodes used to measure resistivity.

FIG. 11 is a multi-electrode apparatus designed to keep certain currentsflowing along the casing in constant in amplitude in the vicinity ofthree spaced apart voltage measurement electrodes used to measureresistivity.

FIG. 12 is an apparatus having three spaced apart voltage measurementelectrodes and extra current introducing electrodes.

FIG. 13 is functionally identical to FIG. 26 from Ser. No. 07/089,697that is U.S. Pat. No. 4,882,542, showing an apparatus having multiplevoltage measurement electrodes engaging the interior of the casing thatis marked with the legend "Prior Art".

The invention is described in three major different portions of thespecification. In the first major portion of the specification, relevantparts of the text in Ser. No. 07/089,697 {Vail(542)} are repeated hereinwhich describe apparatus defined in FIGS. 1, 3, 4, and 5. The secondmajor portion of the specification quotes relevant parts of Ser. No.07/434,886 {Vail(626)} that describe the apparatus defined in FIG. 6.The third major portion of the specification herein is concerned withproviding multi-electrode apparatus and methods of operation of themulti-electrode apparatus to measure formation resistivity from withincased wells that compensates for casing resistance differences and forerrors in placements of the various voltage measurement electrodes. Thedefinitions provided in FIGS. 1 through 6 are used to convenientlydefine many of the symbols appearing in FIGS. 7 through 12.

From a technical drafting point of view, FIGS. 1, 2, 3, 4, and 5 in Ser.No. 07/089,697 {Vail(542)} and in those contained in this applicationare nearly identical. However, the new drawings have been re-done usingcomputer graphics and the A-4 International Size. The following excerptis taken word-for-word from Ser. No. 07/089,697:

"FIG. 1 shows a typical cased borehole found in an oil field. Theborehole 2 is surrounded with borehole casing 4 which in turn is held inplace by cement 6 in the rock formation 8. An oil bearing strata 10exists adjacent to the cased borehole. The borehole casing may or maynot extend electrically to the surface of the earth 12. A voltage signalgenerator 14 (SG) provides an A.C. voltage via cable 16 to poweramplifier 18 (PA). The signal generator represents a generic voltagesource which includes relatively simple devices such as an oscillator torelatively complex electronics such as an arbitrary waveform generator.The power amplifier 18 is used to conduct A.C. current down insulatedelectrical wire 20 to electrode A which is in electrical contact withthe casing. The current can return to the power amplifier through cable22 using two different paths. If switch SW1 is connected to electrode Bwhich is electrically grounded to the surface of the earth, then currentis conducted primarily from the power amplifier through cable 20 toelectrode A and then through the casing and cement layer andsubsequently through the rock formation back to electrode B andultimately through cable 22 back to the power amplifier. In this case,most of the current is passed through the earth. Alternatively, if SW1is connected to insulated cable 24 which in turn is connected toelectrode F, which is in electrical contact with the casing, thencurrent is passed primarily from electrode A to electrode F along thecasing for a subsequent return to the power amplifier through cable 22.In this case, little current passes through the earth.

Electrodes C, D, and E are in electrical contact with the interior ofcasing. In general, the current flowing along the casing varies withposition. For example, current I_(C) is flowing downward along thecasing at electrode C, current I_(D) is flowing downward at electrode D,and current I_(E) is flowing downward at electrode E. In general,therefore, there is a voltage drop V1 between electrodes C and D whichis amplified differentially with amplifier 26. And the voltagedifference between electrodes D and E, V2, is also amplified withamplifier 28. With switches SW2 and SW3 in their closed position asshown, the outputs of amplifiers 26 and 28 respectively aredifferentially subtracted with amplifier 30. The voltage from amplifier30 is sent to the surface via cable 32 to a phase sensitive detector 34.The phase sensitive detector obtains its reference signal from thesignal generator via cable 36. In addition, digital gain controller 38(GC) digitally controls the gain of amplifier 28 using cable 40 to sendcommands downhole. The gain controller 38 also has the capability toswitch the input leads to amplifier 28 on command, thereby effectivelyreversing the output polarity of the signal emerging from amplifier 28for certain types of measurements.

The total current conducted to electrode A is measured by element 42. Inthe preferred embodiment shown in FIG. 1, the A.C. current used is asymmetric sine wave and therefore in the preferred embodiment, I is the0-peak value of the A.C. current conducted to electrode A. (The 0-peakvalue of a sine wave is 1/2 the peak-to-peak value of the sine wave.)

In general, with SW1 connected to electrode B, current is conductedthrough formation. For example, current ΔI is conducted into formationalong the length 2L between electrodes C and E. However, if SW1 isconnected to cable 24 and subsequently to electrode F, then no currentis conducted through formation to electrode B. In this case, I_(C)=I_(D) =I_(E) since essentially little current ΔI is conducted intoformation.

It should be noted that if SW1 is connected to electrode B then thecurrent will tend to flow through the formation and not along theborehole casing. Calculations show that for 7 inch O.D. casing with a1/2 inch wall thickness that if the formation resistivity is 1 ohm-meterand the formation is uniform, then approximately half of the currentwill have flowed off the casing and into the formation along a length of320 meters of the casing. For a uniform formation with a resistivity of10 ohm-meters, this length is 1040 meters instead." These lengths arerespectively called "Characteristic Lengths" appropriate for the averageresistivity of the formation and the type of casing used. ACharacteristic Length is related to the specific length of casingnecessary for conducting on approximately one-half the initial currentinto a particular geological formation as described below.

One embodiment of the invention described in Ser. No. 07/089,697{Vail(542)} provides a preferred method of operation for the aboveapparatus as follows: "The first step in measuring the resistivity ofthe formation is to "balance" the tool. SW1 is switched to connect tocable 24 and subsequently to electrode F. Then A.C. current is passedfrom electrode A to electrode F thru the borehole casing. Even thoughlittle current is conducted into formation, the voltages V1 and V2 arein general different because of thickness variations of the casing,inaccurate placements of the electrodes, and numerous other factors.However, the gain of amplifier 28 is adjusted using the gain controllerso that the differential voltage V3 is nulled to zero. (Amplifier 28 mayalso have phase balancing electronics if necessary to achieve null atany given frequency of operation.) Therefore, if the electrodes aresubsequently left in the same place after balancing for null, spuriouseffects such as thickness variations in the casing do not affect thesubsequent measurements.

With SW1 then connected to electrode B, the signal generator drives thepower amplifier which conducts current to electrode A which is inelectrical contact with the interior of the borehole casing. A.C.currents from 1 amp 0-peak to 30 amps o-peak at a frequency of typically1 Hz are introduced on the casing here. The low frequency operation islimited by electrochemical effects such as polarization phenomena andthe invention can probably be operated down to 0.1 Hz and theresistivity still properly measured. The high frequency operation islimited by skin depth effects of the casing, and an upper frequencylimit of the invention is probably 20 Hz for resistivity measurements.Current is subsequently conducted along the casing, both up and down thecasing from electrode A, and some current passes through the brinesaturated cement surrounding the casing and ultimately through thevarious resistive zones surrounding the casing. The current is thensubsequently returned to the earth's surface through electrode B."

Quoting further from Ser. No. 07/089,697 {Vail(542)}: "FIG. 2 shows thedifferential current conducted into formation ΔI for different verticalpositions z within a steel cased borehole. Z is defined as the positionof electrode D in FIG. 1. It should be noted that with a voltage appliedto electrode A and with SW1 connected to electrode B that this situationconsequently results in a radially symmetric electric field beingapplied to the formation which is approximately perpendicular to thecasing. The electrical field produces outward flowing currents such asΔI in FIG. 1 which are inversely proportional to the resistivity of theformation. Therefore, one may expect discontinuous changes in thecurrent ΔI at the interface between various resistive zones particularlyat oil/water and oil/gas boundaries. For example, curve (a) in FIG. 2shows the results from a uniform formation with resistivity ρ₁. Curve(b) shows departures from curve (a) when a formation of resistivity ρ₂and thickness T₂ is intersected where ρ₂ is less than ρ₁. And curve (c)shows the opposite situation where a formation is intersected withresistivity ρ₃ which is greater than ρ₁ which has a thickness of T₃. Itis obvious that under these circumstances, ΔI₃ is less than ΔI₁, whichis less than ΔI₂.

FIG. 3 shows a detailed method to measure the parameter Vo. ElectrodesA, B, C, D, E, and F have been defined in FIG. 1. All of the numberedelements 2 through 40 have already been defined in FIG. 1. In FIG. 3,the thickness of the casing is τ₁, the thickness of the cement is τ₂,and d is the diameter of the casing. Switches SW1, SW2, and SW3 havealso been defined in FIG. 1. In addition, electrode G is introduced inFIG. 3 which is the voltage measuring reference electrode which is inelectrical contact with the surface of the earth. This electrode is usedas a reference electrode and conducts little current to avoidmeasurement errors associated with current flow.

In addition, SW4 is introduced in FIG. 3 which allows the connection ofcable 24 to one of the three positions: to an open circuit; to electrodeG; or to the top of the borehole casing. And in addition in FIG. 3,switches SW5, SW6, and SW7 have been added which can be operated in thepositions shown. (The apparatus in FIG. 3 can be operated in anidentical manner as that shown in FIG. 1 provided that switches SW2,SW5, SW6, and SW7 are switched into the opposite states as shown in FIG.3 and provided that SW4 is placed in the open circuit position.)

With switches SW2, SW5, SW6, and SW7 operated as shown in FIG. 3, thenthe quantity Vo may be measured. For a given current I conducted toelectrode A, then the casing at that point is elevated in potential withrespect to the zero potential at a hypothetical point which is an"infinite" distance from the casing. Over the interval of the casingbetween electrodes C, D, and E in FIG. 3, there exists an averagepotential over that interval with respect to an infinitely distantreference point. However, the potential measured between only electrodeE and electrode G approximates Vo provided the separation of electrodesA, C, D, and E are less than some critical distance such as 10 metersand provided that electrode G is at a distance exceeding anothercritical distance from the casing such as 10 meters from the boreholecasing. The output of amplifier 28 is determined by the voltagedifference between electrode E and the other input to the amplifierwhich is provided by cable 24. With SW1 connected to electrode B, andSW4 connected to electrode G, cable 24 is essentially at the samepotential as electrode G and Vo is measured appropriately with the phasesensitive detector 34. In many cases, SW4 may instead be connected tothe top of the casing which will work provided electrode A is beyond acritical depth . . . ".

Quoting further from Ser. No. 07/089,697 {Vail(542)}: "For the purposesof precise written descriptions of the invention, electrode A is theupper current conducting electrode which is in electrical contact withthe interior of the borehole casing; electrode B is the currentconducting electrode which is in electrical contact with the surface ofthe earth; electrodes C, D, and E are voltage measuring electrodes whichare in electrical contact with the interior of the borehole casing;electrode F is the lower current conducting electrode which is inelectrical contact with the interior of the borehole casing; andelectrode G is the voltage measuring reference electrode which is inelectrical contact with the surface of the earth.

Furthermore, V_(o) is called the local casing potential. An example ofan electronics difference means is the combination of amplifiers 26, 28,and 30. The differential current conducted into the formation to bemeasured is ΔI." The differential voltage is that voltage in FIG. 1which is the output of amplifier 30 with SW1 connected to electrode Band with all the other switches in the positions shown.

Further quoting from Ser. No. 07/089,697 {Vail(542)}: "FIG. 4 is nearlyidentical to FIG. 1 except the electrodes C and D are separated bylength L₁, electrodes D and E are separated by L₂, electrodes A and Care separated by L₃ and electrodes E and F are separated by the distanceL₄. In addition, r₁ is the radial distance of separation of electrode Bfrom the casing. And Z is the depth from the surface of the earth toelectrode D. FIG. 5 is nearly identical to FIG. 3 except here too thedistances L₁, L₂, L₃, L₄, r₁, and Z are explicitly shown. In addition,r₂ is also defined which is the radial distance from the casing toelectrode G. As will be shown explicitly in later analysis, theinvention will work well if L₁ and L₂ are not equal. And for many typesof measurements, the distances L₃ and L₄ are not very important providedthat they are not much larger in magnitude than L₁ and L₂."

FIG. 6 was first described in Ser. No. 07/434,886 {Vail(626)} whichstates: "For the purpose of logical introduction, the elements in FIG. 6are first briefly compared to those in FIGS. 1-5. Elements No. 2, 4, 6,8, and 10 have already been defined. Electrodes A, B, C, D, E, F, G andthe distances L₁, L₂, L₃, and L₄ have already been described. Thequantities δi₁ and δi₂ have already been defined in the above text.Amplifiers labeled with legends A1, A2, and A3 are analogousrespectively to amplifiers 26, 28, and 30 defined in FIGS. 1, 3, 4, and5. In addition, the apparatus in FIG. 6 provides for the following:

(a) two signal generators labeled with legends "SG 1 at Freq F(1)" and"SG 2 at Freq F(2)";

(b) two power amplifiers labeled with legends "PA 1" and "PA 2";

(c) a total of 5 phase sensitive detectors defined as "PSD 1", "PSD 2","PSD 3", "PSD 4", and "PSD 5", which respectively have inputs formeasurement labeled as "SIG", which have inputs for reference signalslabeled as "REF", which have outputs defined by lines having arrowspointing away from the respective units, and which are capable ofrejecting all signal voltages at frequencies which are not equal to thatprovided by the respective reference signals;

(d) an "Error Difference Amp" so labeled with this legend in FIG. 6;

(e) an instrument which controls gain with voltage, typically called a"voltage controlled gain", which is labeled with legend "VCG";

(f) an additional current conducting electrode labeled with legend "H"(which is a distance L₅ --not shown--above electrode A);

(g) an additional voltage measuring electrode labeled with legend J(which is a distance L₆ --not shown--below electrode F);

(h) current measurement devices, or meters, labeled with legends "I1"and "I2",

(i) and differential voltage amplifier labeled with legend "A4" in FIG.6."

Ser. No. 07/434,886 {Vail(626)} further describes various cables labeledwith legends respectively 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, and 64whose functions are evident from FIG. 6.

Ser. No. 07/434,886 {Vail)626)} further states: "The outputs of PSD 1,2, 3, and 4 are recorded on a digital recording system 70 labeled withlegend "DIG REC SYS". The respective outputs of the phase sensitivedetectors are connected to the respective inputs of the digitalrecording system in FIG. 6 according to the legends labeled with numbers72, 74, 76, 78, and 80. One such connection is expressly shown in thecase of element no. 72."

Ser. No. 07/434,886 {Vail(626)} teaches in great detail that it isnecessary to accurately measure directly, or indirectly, the resistancebetween electrodes C-D (herein defined as "R1") and the resistancebetween electrodes D-E (herein defined as "R2") in FIGS. 1, 3, 4, 5 and6 to precisely measure current leakage into formation and formationresistivity from within the cased well. Please refer to Equations 1-33in Ser. No. 07/434,886 {Vail(626)} for a thorough explanation of thisfact. The parent application, Ser. No. 06/927,115 {Vail(989)} and thefollowing Continuation-in-Part application Ser. No. 07/089,697{Vail(542)} taught that measurement of the resistance of the casingbetween voltage measurement electrodes that engage the interior of thecasing are very important to measure formation resistivity from withinthe casing.

Using various different experimental techniques that result in currentflow along the casing between current conducting electrodes A and F inFIGS. 1, 3, 4, 5, and 6 result in obtaining first compensationinformation related to a first casing resistance defined between voltagemeasurement electrodes C and D. Similarly, using various differentexperimental techniques that result in current flow along the casingbetween current conducting electrodes A and F in FIGS. 1, 3, 4, 5, and 6result in obtaining second compensation information related to a secondcasing resistance between voltage measurement electrodes D and E. FIGS.1, 3, 4, 5, and 6 all provide additional means to cause current to flowinto formation, and the measurements performed while current is flowinginto the formation is called the measurement information related tocurrent flow into formation. Such measurement information is used todetermine a magnitude relating to formation resistivity. FIGS. 7-12 inthe remaining application also provide various means to providemeasurement information, and respectively first and second compensationinformation, along with additional information in several cases.

FIG. 7 is closely related to FIG. 6. However, in FIG. 7, amplifier A3that is shown in FIG. 6, which can be either downhole, or uphole, hasbeen removed. Further, the Error Difference Amp, cable 60, and the VCGhave also been removed. In FIG. 7, the output of amplifier A1 atfrequency F(l) is measured by PSD 4 and the output of amplifier A1 atfrequency F(2) is measured by PSD 2--as was the case in FIG. 6. However,in FIG. 7, the output of amplifier A2 at F(1) is measured by PSD 1 andthe output of amplifier A2 at F(2) is measured by PSD 3. In FIG. 7,current at the frequency of F(1) is conducted into formation resultingin measurement information being obtained from PSD 1 and PSD 4. Currentat the frequency of F(2) is caused to flow along the casing betweenelectrodes H and F to provide compensation for casing thicknessvariations and to provide compensation for errors in the placement ofthe voltage measurement electrodes. First compensation informationrelated to the casing resistance between electrodes C and D is obtainedfrom PSD 2. Second compensation information related to the casingresistance between electrodes D and E is obtained from PSD 3. Analogousalgebra exists for the operation of the apparatus in FIG. 7 to Equations1-33 in Ser. No. 07/434,886 {Vail(626)} that provides compensation forcasing resistance differences and for errors of placements of the threespaced apart voltage measurement electrodes C, D, and E.

FIG. 8 is similar to FIG. 7 except that electrode D in FIG. 7 has beenintentionally divided into two separate electrodes D1 and D2. D1 and D2do not overlap and are separated by a distance L9. Electrodes C and D1are separated by distance L1*. Electrodes D2 and E are separated by thedistance L2*. If D(1) and D(2) overlap, then the invention has the usualconfiguration described in FIGS. 1, 3, 4, 5, 6, and 7. Then consider thesituation wherein electrodes D(1) and D(2) do not overlap. Suppose theyare separated by 1 inch. Then suppose that the separation distancebetween C to D(1) is 20 inches and suppose that the separation distancebetween D(2) to E is also 20 inches. Then clearly, the invention willstill work, although there will be some error in the current leakagemeasurement caused by the lack of measurement information from the 1inch segment. Perhaps the error shall be on the order of 1 inch dividedby 20 inches, or on the order of an approximate 5% error. FIG. 8 showsan apparatus having four spaced apart voltage measurement electrodesthat compensates for casing thickness variations and for errors inplacements of electrodes by providing measurements of the casingresistance R1 between electrodes C and D1 at the frequency of F(2) byPSD 2 and by providing measurements of the casing resistance R2 betweenelectrodes D2 and E at the frequency F(2) by PSD 3.

FIG. 8 may be operated in a particularly simple manner. The signalbetween electrodes C-D1 can be used to control current flowing along thecasing at the frequency F(1) (by using electronics, not shown, of thetype used to control currents in FIG. 6). Then the signal betweenelectrodes D2-E can be used to measure information related to currentflow along the casing and into the formation at the frequency of F(1).Despite the fact that electrodes C-D1 are used to "control current",nonetheless, the apparatus so described requires at least 3 spaced apartvoltage measurement electrodes and is therefore another embodiment ofthe invention herein.

FIG. 9 shows certain changes to the apparatus defined in FIG. 8. Changesfrom FIG. 8 includes cables 88 and 90 that are meant to convey signalsto the appropriate phase sensitive detectors shown in FIG. 8 for thepurposes of simplicity; extra variable resistor labeled with legend"VR1" placed in series with current meter labeled with legend "I1"connected to cable 92 that provides current at the frequency of F(1) tothe upper current conducting electrode here defined as A1; extravariable resistor labeled with legend "VR2" placed in series withanother current meter labeled with legend "I3" connected to cable 94that provides current at the frequency of F(1) to new electrode A2.Electrodes H and F are shown connected to cables 98 and 100 respectivelywhich operate as shown in FIG. 8, but many of the details are omitted inFIG. 9 in the interest of simplicity. In FIG. 9, current at thefrequency of F(2) is passed between electrodes H and F as in FIG. 8which provides first compensation information related to current flowthrough the casing resistance ("R1") between electrodes C-D1 and secondcompensation information related to current flow through the casingresistance ("R2") between electrodes D2-E, although many of the detailsare not shown in FIG. 9 for the purposes of simplicity. The purpose ofelectrodes A1 and A2 in FIG. 9 are to provide simultaneously upward anddownward flowing currents along the casing at the frequency of F(1).Such simultaneously upward and downward flowing currents along thecasing are hereinafter defined as "counter-flowing currents". Suchcounter-flowing currents in the vicinity of the voltage measurementelectrodes C, D1, D2, and E minimize the "common mode signal" input tothe amplifiers A1 and A2. Therefore, the signal output of amplifiers A1and A2 in the presence of such counter-flowing currents tends to be moreresponsive to the current actually flowing into formation and lessresponsive to the relatively larger currents flowing along the casing.Other apparatus showing methods of introducing counter-flowing currentson the casing include FIGS. 22 and 23 of Ser. No. 07/089,697{Vail(542)}. The current actually flowing into the formation at thefrequency of F(1) generates voltages across amplifiers A1 and A2responsive to the current flow into formation that results inmeasurement information at the frequency of F(1) from phase sensitivedetectors as shown in FIG. 8. That measurement information is used todetermine a magnitude relating to formation resistivity, includinginformation related to the resistivity of the adjacent geologicalformation.

FIG. 10 improves the measurement accuracy of the apparatus defined inFIG. 9. FIG. 10 is similar to FIG. 9 except that in FIG. 10 extravoltage measurements P, Q, R, and S have been added. The purpose ofadditional voltage measurement electrodes P and Q are to sense thecurrent flowing along the casing at the frequency of F(1) between P andQ. Further electronics, not shown, are used to control the variableresistor VR1 such that the current flowing along the casing remainsrelatively constant at the frequency of F(1). Please recall thatelectrodes H and F are used to conduct current along the casing at thefrequency of F(2) and therefore, measurements of the potentialdifference between P and Q can be used to measure the casing resistancebetween P and Q that is called "R3" which is therefore used as necessaryinformation to keep the current flowing at the frequency F(1) throughR3. FIG. 6 has already provided means to maintain equality of currentsflowing along the casing, and similar apparatus can be adapted herein tomaintain the equality of current flow at the frequency of F(1) between Pand Q. Similarly comments can be made regarding new electrodes R and Swhich can be used to keep the current flowing along the casing at thefrequency of F(1) constant through the casing resistance betweenelectrodes R and S, that is "R4" by controlling the variable resistorVR2. If the current flowing through R3 at F(1) is held constant as thedevice vertically logs the well, then that shall serve to minimize theinfluence of the lack of information caused by the separation ofelectrodes D1 and D2. Similarly, if the current flowing through R4 atF(1) is held constant, that too serves to minimize the influence of thelack of information caused by the separation between electrodes D1 andD2. Consequently, extra current control means have been provided tocontrol the current flow along the casing at the F(1) to minimize theinfluence of the lack of information from portions of the casing havingno voltage measurement electrodes present. With suitably addedamplifiers, these new electrode pairs can be used to independentlymonitor the counter-flowing currents at the measurement frequency at thepositions shown. In particular, electrode pairs P-Q and R-S can beprovided with amplifiers and feedback circuitry that drives the currentsto A1 and A2 such that the counter-flowing current at the measurementfrequency (for example, 1 Hz) is driven near zero across the voltagemeasurement electrodes C-D1 and D2-E. Regardless of the details ofoperation chosen however, the invention disclosed in FIG. 10 providesfour spaced electrodes means that provides measurement informationrelated to current flow into formation, and respectively, first andsecond compensation information related to measurements of R1 and R2between respectively electrodes C-D, and D-E that are used to determinea magnitude related to formation resistivity. Altogether, FIG. 10 showsa total of 8 each voltage measurement electrodes operated as 4 pairs ofvoltage measurement electrodes.

FIG. 11 is similar to FIG. 10 except that electrodes D1 and D2 have beenre-combined back into one single electrode D herein. However, the extrapotential voltage measurement electrodes P-Q, and R-S remain in FIG. 11to maintain equality of the magnitude of the counter-flowing currentsalong the casing at the frequency of F(1). Maintaining the equality ofcounter-flowing currents along the casing at F(1), and ideally causingthe counter-flowing currents to approach the limit of zero net currentflowing up or down the casing at the frequency of F(1) will result inimproved measurement accuracy. Regardless of the details of operationchosen however, the invention disclosed in FIG. 11 provides a minimum of3 spaced electrodes means that provides measurement information relatedto current flow into formation, and respectively, first and secondcompensation information related to measurements of R1 and R2 betweenrespectively electrodes C-D, and D-E that are used to determine amagnitude related to formation resistivity. Altogether, FIG. 11 shows atotal of 7 each voltage measurement electrodes operated as 4 pairs ofvoltage measurement electrodes.

FIG. 12 is similar to FIG. 11 except that the extra potential voltagemeasurement electrodes P-Q and R-S have been removed. It should be notedthat the apparatus defined in FIG. 12 results in knowledge of themeasurement current leaking into formation, knowledge of the resistanceR1 between voltage measurement electrodes C-D, and the knowledge of theresistance R2 between voltage measurement electrodes D-E. Therefore, theapparatus in FIG. 12 provides knowledge of the net current at F(1)flowing through resistor R1 between electrodes C-D. Similarly, theapparatus in FIG. 12 provides knowledge of the net current at F(1)flowing through resistor R2 between electrodes D-E. Extra controlcircuitry, not shown, can be adapted as in FIG. 6 to minimize the netcounter-flowing currents flowing by the combined resistors R1 and R2 toimprove measurement accuracy. Regardless of the details of operationchosen however, the invention disclosed in FIG. 12 provides a minimum of3 spaced apart electrode means that provide measurement informationrelated to current flow into formation, and respectively, first andsecond compensation information related to measurements of R1 and R2between respectively electrodes C-D, and D-E that are used to determinea magnitude related to formation resistivity.

The apparatus in FIG. 12 may be operated in a particularly simplemanner. Information from pair C-D can be used to control the magnitudeof the current flowing along the casing at the frequency of F(1), andkeep it constant. Then information from pair D-E can be used to infergeophysical parameters from measurements of the current at the frequencyof F(1). Despite the fact that the first pair C-D is used primarilyherein "to control current", the apparatus so described nonethelessrequires 3 spaced apart voltage measurement electrodes which engage theinterior of the casing and is therefore simply another embodiment of theinvention herein.

FIG. 13 is functionally identical to FIG. 26 from Ser. No. 07/089,697that is U.S. Pat. No. 4,882,542, showing an apparatus having multiplevoltage measurement electrodes engaging the interior of the casing thatis marked with the legend "Prior Art". Individual potential voltagemeasurement electrodes k, l, m, n, o, p, q, r, s, and t electricallyengage the casing. In principle, any total number Z of such potentialvoltage measuring electrodes can be made to electrically engage theinterior of the casing. During the calibration step described inVail(542), current is passed along the casing resulting in the knowledgeof the respective casing resistances between each potential voltagemeasurement electrode. The casing resistance between electrodes k and lis defined herein as R(k,l). The casing resistance between electrodes land m is defined herein as R(l,m). The casing resistance between m and nis defined herein R(m,n). The casing resistance between n and o isdefined herein as R(n,o). By analogy, the casing resistances R(o,p),R(p,q), R(q,r), R(r,s) and R(s,t) are defined herein. In principle, anynumber of casing resistances can be defined for any number Z ofelectrodes which electrically engage the interior of the casing. Thedistance along the casing between electrodes k and l is defined hereinas L(k,l). The distance along the casing between electrodes l and m isdefined herein as L(l,m). The distance along the casing betweenelectrodes m and n is defined herein as L(m,n). The distance along thecasing between electrodes n and o is defined herein as L(n,o). Byanalogy, the distances of separation of appropriate electrodes aredefined herein as L(o,p), L(p,q), L(q,r), L(r,s,) and L(s,t). Inprinciple, any number of distances can be defined between any number Zelectrodes which electrically engage the interior of the casing. Thedistance of separation between electrodes can be chosen to be anydistance. They may be chosen to be equal or they can be chosen not to beequal, depending upon chosen function. For example, L(k,l) can be chosento be 3 inches. L(l,m) can be chosen to be 6 inches. L(m,n) can bechosen to be 12 inches. L(n,o) can be chosen to be 20 inches. L(o,p) canbe chosen to be 52 inches. L(p,q) can be chosen to be 60 inches. L(q,r)can be chosen to be 120 inches. Further, electrodes s and t can bedisconnected. Such an array can measure the potential voltagedistribution along the casing or the potential voltage profile along thecasing in response to calibration currents primarily flowing along thecasing and in response to the measurement currents flowing along thecasing and into the formation. The calibration current can be at chosento be the same frequency as the measurement current as originallydescribed in Vail(989) or can be at a different frequency as describedin Vail(626). The above described variable spacing can be used to inferthe vertical and radial variations of the geological formation, thevertical distribution of geological beds, and other geologicalinformation. Regardless of the details of operation chosen however, theinvention disclosed in FIG. 13 provides a minimum of 3 spaced apartvoltage measurement electrode means that provide measurement informationrelated to current flow into formation, and respectively, first andsecond compensation information related to measurements of at least twocasing resistances respectively between the three voltage measurementelectrodes, wherein said measurement information and the first andsecond compensation information are used to determine a magnituderelated to formation resistivity. FIG. 12 and the text herein furthershows that a plurality of spaced apart electrodes along the casing,which may be chosen to be spaced at various different intervals, providemultiple measurements of quantities related to current flow intoformation, and provide multiple measurements of the resistances of thecasing spanned by the particular number of chosen spaced apartelectrodes that may be used to infer geophysical information includingthe resistivity of the adjacent formation.

It should also be noted that Ser. No. 07/089,697 {Vail(542)} describesmany different means to measure voltage profiles on the casing includingthose shown in FIG. 25, 26, 27, 28, and 29 therein. Those drawingsdescribe several other apparatus geometries having multiple electrodes.

Various embodiments of the invention herein provide many differentmanners to introduce current onto the casing, a portion of which issubsequently conducted through formation. Various embodiments hereinprovide many different methods to measure voltage levels at a pluralityof many points on the casing to provide a potential voltage profilealong the casing which may be interpreted to measure the current leakingoff the exterior of the casing from within a finite vertical section ofthe casing. Regardless of the details of operation chosen however, theinvention herein disclosed provides a minimum of 3 spaced apart voltagemeasurement electrode means that provides measurement informationrelated to current flow into the geological formation, and respectively,first and second compensation information related to measurements of atleast two separate casing resistances between the three spaced apartvoltage measurement electrodes, wherein the measurement information andthe first and second compensation information are used to determine amagnitude related to formation resistivity.

While the above description contains many specificities, these shouldnot be construed as limitations on the scope of the invention, butrather as exemplification of preferred embodiments thereto. As has beenbriefly described, there are many possible variations. Accordingly, thescope of the invention should be determined not only by the embodimentsillustrated, but by the appended claims and their legal equivalents.

What is claimed is:
 1. An apparatus for determining the resistivity of ageological formation from within a cased well, comprising:a firstelectrode that electrically engages a first particular section of casingat a specific depth within the well for receiving first signals havingvoltage related information; a second electrode that electricallyengages the first particular section of casing for receiving secondsignals having voltage related information located a first distanceabove said first electrode wherein the magnitude of the resistance ofthe portion of casing between said first and second electrodes is thefirst resistance; a third electrode that electrically engages the firstparticular section of casing for receiving third signals having voltagerelated information located a second distance below said first electrodewherein the magnitude of the resistance of the portion of casing betweensaid first and third electrodes is the second resistance; a fourthelectrode that electrically engages the casing at a point located athird distance above said second electrode; a fifth electrode thatelectrically engages the casing at a point located a fourth distanceabove said fourth electrode; a sixth electrode that electrically engagesthe casing at a point located a fifth distance about said fifthelectrode; a seventh electrode that electrically engages the surface ofthe earth; means to conduct a first current from said sixth electrode tosaid seventh electrode; constant current control means to measure and tocontrol the magnitude of the portion of the first current flowingthrough a second portion of the casing located between said fourth andfifth electrodes so that the magnitude of said portion of the firstcurrent is equal to a predetermined selected constant value; means tomeasure said first resistance and said second resistance; means forprocessing said first, second and third signals from said first, secondand third electrode means for use in determining the resistivity of theformation of interest, said means for processing taking into account amagnitude relating to the values of said first resistance and saidsecond resistance so that inaccuracy associated with the determinationof the resistivity is reduced.
 2. A method for determining theresistivity of a geological formation from within a cased well,comprising:providing an apparatus having a first electrode thatelectrically engages a first particular section of casing for receivingfirst voltage related signals at a specific depth within the well; saidapparatus having a second electrode that electrically engages the firstparticular section of casing for receiving second voltage relatedsignals located a first distance above said first electrode wherein themagnitude of the resistance of the portion of casing between said firstand second electrodes is the first resistance; and said apparatus havinga third electrode that electrically engages the first particular sectionof casing for receiving third voltage related signals located a seconddistance below said first electrode wherein the magnitude of theresistance of the portion of casing between said first and thirdelectrodes is the second resistance; said apparatus having a fourthelectrode that electrically engages the casing at a point located athird distance above said second electrode; said apparatus having afifth electrode that electrically engages the casing at a point locateda fourth distance above said fourth electrode; said apparatus having asixth electrode that electrically engages the casing at a point locateda fifth distance above said fifth electrode; said apparatus having aseventh electrode that electrically engages the surface of the earth;said apparatus having means to conduct a first current between saidsixth and seventh electrodes; said apparatus having constant currentcontrol means to measure and to control the magnitude of the portion ofsaid first current flowing through a second portion of the casinglocated between said fourth and fifth electrodes; said apparatus havingmeans to measure said first resistance and said second resistance;conducting first current from said sixth electrode through the formationto said seventh electrode; choosing the portion of said first currentflowing through the second portion of casing to be equal to apredetermined selected constant value; obtaining said first, second, andthird voltage related signals while conducting said first current intothe formation; determining the magnitude of said first resistance andsaid second resistance; and processing the voltage related signals fromeach of said first, second and third electrodes for use in determiningthe resistivity of the geological formation of interest, said processingtaking into account the determined magnitudes of said first resistanceand said second resistance to reduce the inaccuracy associated with thedetermination of the resistivity of the geological formation ofinterest.
 3. An apparatus for determining the resistivity of ageological formation from within a cased well, comprising:a firstelectrode that electrically engages a first particular section of casingat a specific depth within the well for receiving first signals havingvoltage related information; a second electrode that electricallyengages the first particular section of casing for receiving secondsignals having voltage related information located a first distanceabove said first electrode wherein the magnitude of the resistance ofthe portion of casing between said first and second electrodes is thefirst resistance; a third electrode that electrically engages the casingat a point located a second distance above said second electrode; afourth electrode that electrically engages the surface of the earth;means to conduct a first current from said third electrode to saidfourth electrode; constant current control means to measure and tocontrol the magnitude of the portion of the first current flowingthrough a second portion of the casing located between said second andthird electrodes so that the magnitude of said portion of the firstcurrent is equal to a predetermined selected constant value; means tomeasure said first resistance; means for processing said first andsecond signals from said first and second electrode means for use indetermining the resistivity of the formation of interest, said means forprocessing taking into account a magnitude relating to the value of saidfirst resistance and said selected constant value of said portion of thefirst current so that inaccuracy associated with the determination ofthe resistivity is reduced.
 4. A method for determining the resistivityof a geological formation from within a cased well, comprising:providingan apparatus having a first electrode that electrically engages a firstparticular section of casing for receiving first voltage related signalsat a specific depth within the well; said apparatus having a secondelectrode that electrically engages the first particular section ofcasing for receiving second voltage related signals located a firstdistance above said first electrode wherein the magnitude of theresistance of the portion of casing between said first and secondelectrodes is the first resistance; and said apparatus having a thirdelectrode that electrically engages the casing at a point located asecond distance above said second electrode; said apparatus having afourth electrode that electrically engages the surface of the earth;said apparatus having means to conduct a first current between saidthird and fourth electrodes; said apparatus having constant currentcontrol means to measure and to control the magnitude of the portion ofsaid first current flowing through a second portion of the casinglocated between said second and third electrodes; said apparatus havingmeans to measure said first resistance; conducting first current fromsaid third electrode through the formation to said fourth electrode;choosing the portion of said first current flowing through the secondportion of casing to be equal to a predetermined selected constantvalue; obtaining said first, and second voltage related signals whileconducting said first current into the formation; determining themagnitude of said first resistance; processing the voltage relatedsignals from each of said first and second electrodes for use indetermining the resistivity of the geological formation of interest,said processing taking into account the determined magnitude of saidfirst resistance and said predetermined selected constant value of saidportion of the first current to reduce the inaccuracy associated withthe determination of the resistivity of the geological formation ofinterest.
 5. A method for determining the resistivity of a geologicalformation from within a cased well, comprising:providing an apparatushaving a first electrode that electrically engages a first particularsection of casing for receiving first voltage related signals at aspecific depth within the well; said apparatus having a second electrodethat electrically engages the first particular section of casing forreceiving second voltage related signals located a first distance abovesaid first electrode wherein the magnitude of the resistance of theportion of casing between said first and second electrodes is the firstresistance; whereby said first and second electrodes comprise a firstpair of voltage measurement electrodes; said apparatus having a thirdelectrode that electrically engages a second particular section ofcasing for receiving third voltage related signals located a seconddistance above said second electrode; said apparatus having a fourthelectrode that electrically engages the second particular section ofcasing for receiving fourth voltage related signals located a thirddistance above said third electrode wherein the magnitude of theresistance of the second portion of casing between said third and fourthelectrodes is the second resistance; whereby said third and fourthelectrodes comprise a second pair of voltage measurement electrodes;said apparatus having a fifth electrode that electrically engages thecasing at a point located a fourth distance above said fourth electrode;said apparatus having a sixth electrode that electrically engages thesurface of the earth; said apparatus having means to conduct a firstcurrent between said fifth and sixth electrodes; said apparatus havingconstant current control means to measure and to control the magnitudeof the portion of said first current flowing through the second portionof the casing; said apparatus having means to measure said firstresistance; said apparatus having means to measure said secondresistance; conducting first current from said fifth electrode throughthe formation to said sixth electrode; choosing the portion of saidfirst current flowing through the second portion of casing to be equalto a predetermined selected constant value; obtaining said first andsecond voltage related signals while conducting said first current intothe formation; determining the magnitude of said first resistance;processing the voltage related signals from each of said first andsecond electrodes for use in determining the resistivity of thegeological formation of interest, said processing taking into accountthe determined magnitude of said first resistance and said predeterminedselected constant value of said portion of the first current to reducethe inaccuracy associated with the determination of the resistivity ofthe geological formation of interest.
 6. The method as in claim 5wherein the first pair of electrodes are separated by a first pairdistance and the second pair of electrodes are separated by a secondpair distance.
 7. The method as in claim 6 wherein the first and secondpair distances are equal.
 8. A method for determining the resistivity ofa geological formation from within a cased well, comprising at least thefollowing steps:(a) generating and causing a constant current to flowalong a first particular section of casing at a first depth; (b)measuring the current leakage into formation from a second particularsection of casing at a second depth, whereby said second particularsection of casing is located below said first particular section ofcasing by a constant distance of separation; (c) repetitively measuringthe current leakage into formation by choosing first and second depthsto be separated by the constant distance of separation; and (d) using atleast information related to current leakage into formation for use indetermining the resistivity of the geological formation of interest. 9.An apparatus for determining the resistivity of a geological formationfrom within a cased well, comprising at least the following:(a) means togenerate and cause a constant current to flow along a first particularsection of casing at a first depth; (b) means to measure the currentleakage into formation from a second particular section of casing at asecond depth, whereby said second particular section of casing islocated above said first particular section of casing by a constantdistance of separation; (c) means to measure the current leakage intoformation by choosing said first and second depths to be separated bythe constant distance of separation; and (d) means to measure at leastinformation related to current leakage into formation to determine theresistivity of the geological formation of interest.
 10. A method fordetermining the resistivity of a geological formation from within acased well, comprising at least the following steps:(a) generating andcausing a constant current to flow along a first particular section ofcasing at a first depth; (b) measuring the current leakage intoformation from a second particular section of casing at a second depth;(c) repetitively generating said constant current at different firstdepths and measuring said current leakage at different second depths;and (d) using at least information related to current leakage intoformation to determine the resistivity of the formation of interest. 11.Apparatus for determining the resistivity of a geological formation fromwithin a cased well comprising at least:(a) means to generate a constantcurrent to flow along a first predetermined section of casing; (b) meansto measure the current leakage into the geological formation from asecond predetermined section of casing; and (c) means to measure atleast information related to current leakage into formation to determinethe resistivity of the geological formation of interest.